In "The Martian", when Johanssen speaks to her father about possibly having to eat the crew if the probe fails, why does she say it would take 17 months to return alone? If the probe failed, wouldn't she be right outside of Earth's orbit?
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5Space doesn't really work like that. She'd be right by earth but going far too fast to stop (I'm going by memory but I think they were supposed to be on reverse trust for a month before reaching earth - which they didn't do, opting for a slingshot around earth instead). Where you are does matter but your velocity often matters more– user20310Commented Jan 3, 2016 at 0:28
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So you're saying it would take 17 months to decelerate and turn around?– John smithCommented Jan 3, 2016 at 0:39
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IIRC 17 months was the required roundtrip slingshot on Earth, back to Mars, flyby and turnaround, and back to Earth, with required deceleration. Failing the probe rendezvous only meant, not enough food to keep all the astronauts alive...– IgnazioCommented Jan 3, 2016 at 4:19
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1@user20310: Belongs down there in the answer section, no?– Lightness Races in OrbitCommented Jan 3, 2016 at 18:17
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@LightnessRacesinOrbit True, my comment was a little too unsubstatiated to post as an answer but as noone has answered in the meantime I've flushed my comment out as an answer– user20310Commented Jan 3, 2016 at 20:16
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1 Answer
Space doesn't really work like that. She'd be right by earth but going far too fast to stop (or more precisely enter orbit).
Under the original course they would have entered earth orbit (which presumably would have involved a lengthy deceleration on the approach to earth). Instead they made the "Rich Purnell Maneuver" which commits them to making a sling shot maneuver around earth, never actually entering orbit, and heading back in the direction of Mars.
Lewis states that the maneuver once made can't be unmade
"yes", Lewis confirmed, "thats exactly what we're talking about. If we go through with the maneuver, they'll have to send the supply or we'll die. We have have the opportunity to force their hand"
This is confirmed by mission control (or at least heavily implied)
"Work out how long they can stay on this course before its irreversible. At what point will they no longer be able to intercept earth?"
So Johanssen will be in the rough vicinity of earth, but assuming "smashing into the earth in a terrible fireball" is not an acceptable option she also needs to have her velocity "in the rough vicinity of earth's" as well, which with the available thrust is not possible.
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1As a bonus, you can see Andy Weir describe the "Rich Purnell Maneuver" trajectory: youtu.be/gMfuLtjgzA8?t=17m26s Commented Jan 3, 2016 at 20:49